SQL Server 2019

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-- declare vars
DECLARE @dateToCheck    date = '2020-09-20'
DECLARE @numRecsBefore  int = 0 
DECLARE @numRecsAfter   int = 0
DECLARE @tempID         int

-- temp table
CREATE TABLE #dates
    (
    [idx]       INT IDENTITY(1,1),
    [startDate] DATETIME ,
    [endDate]   DATETIME,
    [prevEndDate] DATETIME
    )

-- insert temp table
INSERT INTO #dates 
        ( [startDate], [endDate] )
VALUES  ( '2020-09-01', '2020-09-04' ),
        ( '2020-09-04', '2020-09-10' ),
        ( '2020-09-10', '2020-09-16' ),
        ( '2020-09-17', '2020-09-19' ),
        ( '2020-09-19', '2020-09-20' ),
        --
        ( '2020-09-20', '2020-09-23' ),
        ( '2020-09-25', '2020-09-26' ),
        ( '2020-09-27', '2020-09-28' ),
        ( '2020-09-28', '2020-09-30' ),
        ( '2020-10-01', '2020-09-05' )
;

select 
	max(case when @dateToCheck > startdate  and @dateToCheck <= enddate then numRecsBefore end) as numRecsBefore,
	max(case when @dateToCheck >= startdate  and @dateToCheck < enddate then numRecsAfter end) as numRecsAfter
from (
	select d.*, 
		count(*) over(partition by grp order by startdate) as numRecsBefore,
		count(*) over(partition by grp order by startdate desc) as numRecsAfter
	from (
		select d.*,
			sum(case when startdate = lag_enddate then 0 else 1 end) over(order by startdate) as grp
		from (
			select d.*,
				lag(enddate) over(order by startdate) as lag_enddate
			from #dates d
		) d
	) d
) d;

numRecsBefore	numRecsAfter
2	1

Warning: Null value is eliminated by an aggregate or other SET operation.